document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1173649>Question 1173649</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A major city wants to establish a sinking fund to pay off debts of PKR 800 million which come<BR>\n" );
document.write( "due in 10 years. The city can earn interest at the rate of 8 percent per year compounded monthly.\r<BR>\n" );
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document.write( "If first deposit is made 1 month from now;<BR>\n" );
document.write( "a) What monthly deposit will be required to accumulate the PKR 800 million?<BR>\n" );
document.write( "b) How much interest will be earned on these deposits </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850724 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=850724\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Absolutely, let's break down this sinking fund problem step-by-step:\r<BR>\n" );
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document.write( "**Understanding the Problem**\r<BR>\n" );
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document.write( "* **Future Value (FV):** PKR 800,000,000 (the amount needed in 10 years)<BR>\n" );
document.write( "* **Annual Interest Rate (r):** 8% or 0.08<BR>\n" );
document.write( "* **Compounding Frequency (n):** Monthly (12 times per year)<BR>\n" );
document.write( "* **Time Period (t):** 10 years\r<BR>\n" );
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document.write( "**Calculations**\r<BR>\n" );
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document.write( "**a) Monthly Deposit Calculation**\r<BR>\n" );
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document.write( "1.  **Monthly Interest Rate (i):**<BR>\n" );
document.write( "    * i = r / n = 0.08 / 12 = 0.00666667 (approximately)\r<BR>\n" );
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document.write( "2.  **Total Number of Periods (N):**<BR>\n" );
document.write( "    * N = n * t = 12 * 10 = 120 months\r<BR>\n" );
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document.write( "3.  **Sinking Fund Formula:**<BR>\n" );
document.write( "    * The monthly deposit (PMT) can be calculated using the following formula:<BR>\n" );
document.write( "        * PMT = FV * (i / ((1 + i)^N - 1))\r<BR>\n" );
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document.write( "4.  **Applying the Values:**<BR>\n" );
document.write( "    * PMT = 800,000,000 * (0.00666667 / ((1 + 0.00666667)^120 - 1))<BR>\n" );
document.write( "    * PMT = 4,372,874.22 PKR\r<BR>\n" );
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document.write( "Therefore, the city will need to deposit approximately PKR 4,372,874.22 each month.\r<BR>\n" );
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document.write( "**b) Total Interest Earned**\r<BR>\n" );
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document.write( "1.  **Total Deposits:**<BR>\n" );
document.write( "    * Total Deposits = PMT * N = 4,372,874.22 * 120 = 524,744,905.81 PKR\r<BR>\n" );
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document.write( "2.  **Total Interest:**<BR>\n" );
document.write( "    * Total Interest = FV - Total Deposits = 800,000,000 - 524,744,905.81 = 275,255,094.19 PKR\r<BR>\n" );
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document.write( "Therefore, the city will earn approximately PKR 275,255,094.19 in interest over the 10 years.\r<BR>\n" );
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document.write( "**Summary**\r<BR>\n" );
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document.write( "* **Monthly Deposit:** PKR 4,372,874.22<BR>\n" );
document.write( "* **Total Interest Earned:** PKR 275,255,094.19<BR>\n" );
document.write( " </SPAN>\n" );
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